Eur. Phys. J. B (2014) 87: 269
https://doi.org/10.1140/epjb/e2014-50174-5

Regular Article

Quantization, coherent states and geometric phases of a generalized nonstationary mesoscopic RLC circuit

Departamento de Física, CCEN, Universidade Federal da Paraíba, Caixa Postal 5008, 58059-900 João Pessoa, PB, Brazil

^a e-mail: iapedrosa@fisica.ufpb.br

Received: 14 March 2014
Received in final form: 7 July 2014
Published online: 17 November 2014

Abstract

We present an alternative quantum treatment for a generalized mesoscopic RLC circuit with time-dependent resistance, inductance and capacitance. Taking advantage of the Lewis and Riesenfeld quantum invariant method and using quadratic invariants we obtain exact nonstationary Schrödinger states for this electromagnetic oscillation system. Afterwards, we construct coherent and squeezed states for the quantized RLC circuit and employ them to investigate some of the system’s quantum properties, such as quantum fluctuations of the charge and the magnetic flux and the corresponding uncertainty product. In addition, we derive the geometric, dynamical and Berry phases for this nonstationary mesoscopic circuit. Finally we evaluate the dynamical and Berry phases for three special circuits. Surprisingly, we find identical expressions for the dynamical phase and the same formulae for the Berry’s phase.